Question

Specimen 1 2 3 4 5 6 7 8 9

Steel ball 50 57 61 70 68 54 65 51 53

Diamond 52 55 63 74 69 55 68 51 56

The manufacturer of hardness testing equipment uses​ steel-ball indenters to penetrate metal that is being tested.​ However, the manufacturer thinks it would be better to use a diamond indenter so that all types of metal can be tested. Because of differences between the two types of​ indenters, it is suspected that the two methods will produce different hardness readings. The metal specimens to be tested are large enough so that two indentions can be made.​Therefore, the manufacturer uses both indenters on each specimen and compares the hardness readings. Construct a​ 95% confidence interval to judge whether the two indenters result in different measurements.

​Note: A normal probability plot and boxplot of the data indicate that the differences are approximately normally distributed with no outliers.

Construct a​ 95% confidence interval to judge whether the two indenters result in different​ measurements, where the differences are computed as​ 'diamond minus steel​ ball'.

Answer 1

n1 = n2 = n = 9, d-bar = 1.5556, s = 1.8105, Confidence level = 95%

Degrees of freedom = n - 1 = 8

SE = s/√n = 0.6035

t- score = 2.306004133

Margin of error = t * SE = 1.3917

The 95% confidence interval is [1.5556 - 1.3917, 1.5556 + 1.3917] = [0.164, 2.947]

The above confidence interval does not contain 0. This means there is enough evidence that the two indenters result in significantly different measurements.

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